Conventional computers are highly attuned to using operations that require manipulating ordinal numbers, especially ordinal binary integers. The value of an ordinal number corresponds with its position in a set of sequentially ordered number values. These computers use ordinal binary integers to represent, manipulate, and store information. These computers rely on the numerical order of ordinal binary integers representing data to perform various operations such as counting, sorting, indexing, and mathematical calculations. Even when performing operations that involve other number systems (e.g. floating point), conventional computers still resort to using ordinal binary integers to perform any operations.
Ordinal based number systems only provide information about the sequence order of the numbers themselves based on their numeric values. Ordinal numbers do not provide any information about any other types of relationships for the data being represented by the numeric values such as similarity. For example, when a conventional computer uses ordinal numbers to represent data samples (e.g. images or audio signals), different data samples are represented by different numeric values. The different numeric values do not provide any information about how similar or dissimilar one data sample is from another. Unless there is an exact match in ordinal number values, conventional systems are unable to tell if a data sample matches or is similar to any other data samples. As a result, conventional computers are unable to use ordinal numbers by themselves for comparing different data samples and instead these computers rely on complex signal processing techniques. Determining whether a data sample matches or is similar to other data samples is not a trivial task and poses several technical challenges for conventional computers. These technical challenges result in complex processes that consume processing power which reduces the speed and performance of the system. The ability to compare unknown data samples to known data samples is crucial for many security applications such as face recognition, voice recognition, and fraud detection.
Thus, it is desirable to provide a solution that allows computing systems to efficiently determine how similar different data samples are to each other and to perform operations based on their similarity.